P(t)=105t(0.81^t)

Solution for P(t)=105t(0.81^t) equation:

(P)=105P(0.81^P)

We move all terms to the left:

(P)-(105P(0.81^P))=0


We calculate terms in parentheses: -(105P(0.81^P)), so:

105P(0.81^P)

We multiply parentheses

0P^2

We add all the numbers together, and all the variables

P^2

Back to the equation:

-(P^2)


determiningTheFunctionDomain
-P^2+P=0

We add all the numbers together, and all the variables

-1P^2+P=0

a = -1; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-1)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-1}=\frac{-2}{-2}
=1
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-1}=\frac{0}{-2}
=0
$